Dear GAP Forum,

The recently released bugfixes fixed a number of *dangerous* bugs in GAP, that
is bugs that could cause a computation to produce a wrong result without
warning. Although we think it unlikely, this could result in users having
arrived at plausible but incorrect mathematical results. To help you decide if
you might be in this position, this mail gives more details of the exact
effect of the bugs, and the dates on which they were introduced into GAP.

One of these bugs dates from GAP 3.1, and we said in the announcement of
bugfix4 that no fix was available for this bug in GAP3. In fact we now have a
fix, and will release it as soon as possible. Since this is the first change
to the GAP3 kernel for more than two years, you will appreciate that getting
all the necessary versions compiled, and preparing the fix is not a routine
task.
In a subsequent announcement, we will say more about our policy for
maintenance of GAP3, but in the meantime, we would urge all users who can to
move to GAP4.

Finite field exponentiation bugs
================================
The first finite field bug:

The bug affected the computation of powers of elements in a finite
field in the following situation and could produce wrong results.

        (Z(q)^m)^n  where m>0, n>0 and m*n > 2^31-1
and 
        (Z(q)^m)^-n where m>0, n>0 and (q-m)*n > 2^31-1

This bug has been there since the first release of GAP 4 and in
fact goes back to the first release of GAP 3. It is fixed by bugfix #4.

The second finite field bug:

Fixing the previous bug introduced another one which also affected
the computation of powers of elements in a finite field in the
following situation:

(0*Z(q))^m was evaluated incorrectly to one when m was a
multiple of q-1.

This bug has been there since bug fix #4.

Polycyclic Groups Bug
=====================

This bug affects PrimePowerComponents for PcGroups (and consequentially
`SpecialPcgs' and everything that builds on top of it) for groups with at
least three distinct primes dividing their order. It was introduced to the
development version in May 1999 and so was released for the first time in GAP
4.1. In particular, the beta versions of GAP 4 did not contain this bug.

Primitive Groups Database Bug
=============================

Among the things fixed in bugfix 4, which were not explicitly mentioned is a
small bugfix to the library of primitive groups.

The error (which was reported by Christial Pech -- many thanks again!)
affected the primitive groups of degree 325 and 756, among these groups were
some which were of the right *isomorphism type* but in the wrong
*permutation representation*, that is they were of the wrong permutation
degree.

This error was due to a misinterpretation of information from the printed
version of the classification of primitive groups in [Dixon, Mortimer].

The error is fixed and tests have been run to ensure that all groups in this
library now are of the right degree.

Steve Linton